[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(-1,2)\qquad B(8,15)\qquad \qquad \stackrel{\textit{ratio from A to B}}{2:1} \\\\\\ \cfrac{A\underline{M}}{\underline{M} B} = \cfrac{2}{1}\implies \cfrac{A}{B} = \cfrac{2}{1}\implies 1A=2B\implies 1(-1,2)=2(8,15)\\\\[-0.35em] ~\dotfill\\\\ M=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf M=\left(\cfrac{(1\cdot -1)+(2\cdot 8)}{2+1}\quad ,\quad \cfrac{(1\cdot 2)+(2\cdot 15)}{2+1}\right) \\\\\\ M=\left( \cfrac{-1+16}{3}~,~\cfrac{2+30}{3} \right)\implies M=\left(\cfrac{15}{3}~,~\cfrac{32}{3} \right)\implies M=\left(5~,~ 10\frac{2}{3} \right)[/tex]
Answer:
C) (5, 32/3)
Step-by-step explanation:
(5, 32/3) The sum of the ratio numbers (2+1) is 3, so M is 2/3 of the distance from A to B. The coordinates of M are (xm, ym), where xm = -1 + 2/3(8 - (1)) and ym = 2 + 2/3(15 - 2).
